Units of Measurement (Including SI Units)

Scientific Notation

Sometimes it is necessary to use very large and very small numbers. These can best be indicated and handled in calculations by use of scientific notation, which is to say by use of exponents. Use of scientific notation requires writing the number so that it is the result of multiplying some whole number power of 10 by a number between 1 and 10. Examples are: 1234 = 1.234 × 103

0.01234 = 1.234 × 1/100 = 1.234 × 10−2

0.001234 = 1.234 × 1/1000 = 1.234 × 10−3

To convert a number to its equivalent in scientific notation:

Place the decimal point to the right of the first non-zero digit. This will now be a number between 1 and 9.

Multiply this number by a power of 10, the exponent of which is equal to the number of places the decimal point was moved. The exponent is positive if the decimal point was moved to the left, and negative if it was moved to the right. For example: 1,234,000.0 × 0.000072/6000.0 = 1.234 × 106× 7.2 × 10 −5/6.0 × 103

Now, by simply adding or subtracting the exponents of ten, and remembering that moving an exponent from the denominator of the fraction to the numerator changes its sign, = 1.234 × 106 × 10 −5 × 10 −3 × 7.2/6 = 1.234 × 10−2 × 7.2/6

The last operation changed 1.4808 × 10−2 into the final value, 0.014808, which is not expressed in scientific notation.

SI Units (Système International d'Unités or International System of Units)

This system includes two types of units important in clinical medicine. The base units are shown in the first table, derived units in the second table, and derived units with special names in the third table.

Weights and Measures

Arabic numerals are used with masses and measures, as 10 g, or 3 mL. Portions of masses and measures are usually expressed decimally. For practical purposes, 1 cm3 (cubic centimeter) is equivalent to 1 mL (milliliter) and 1 drop (gtt.) of water is equivalent to a minim (m).

Note: Traditionally, the word “weights” is used in these tables, but “masses” is the correct term.

LENGTH

Millimeters (mm)

Centimeters (cm)

Inches (in)

Feet (ft)

Yards (yd)

Meters (m)

1.0

0.1

0.03937

0.00328

0.0011

0.001

10.0

1.0

0.3937

0.03281

0.0109

0.01

25.4

2.54

1.0

0.0833

0.0278

0.0254

304.8

30.48

12.0

1.0

0.333

0.3048

914.40

91.44

36.0

3.0

1.0

0.9144

1000.0

100.0

39.37

3.2808

1.0936

1.0

1 μm = 1 micrometer = 0.001 millimeter. 1 mm = 100 μm.

1 km = 1 kilometer = 1000 meters = 0.62137 statute mile.

1 statute mile = 5280 feet = 1.609 kilometers.

1 nautical mile = 6076.042 feet = 1852.276 meters.

VOLUME (FLUID)

Milliliters (mL)

Cubic Inches (in3 )

U.S. Fluid Quarts (qt)

Liters (L)

1.0

0.061

0.00106

0.001

3.697

0.226

0.00391

0.00369

16.3866

1.0

0.0173

0.01639

29.573

1.8047

0.03125

0.02957

946.332

57.75

1.0

0.9463

1000.0

61.025

1.0567

1.0

1 gallon = 4 quarts = 8 pints = 3.785 liters.

1 pint = 473.16 mL.

WEIGHT

Grains (gr)

Grams (g)

Apothecaries' Ounces (f℥)

Kilograms (kg)

1.0

0.0648

0.00208

0.000065

15.432

1.0

0.03215

0.001

480.0

31.1

1.0

0.0311

7000.0

453.5924

14.583

0.45359

15432.358

1000.0

32.15

1.0

1 microgram (μg) = 0.001 milligram.

1 mg = 1 milligram = 0.001 g; 1000 mg = 1 g.

CIRCULAR MEASURE

60 seconds = 1 minute

60 minutes = 1 degree

90 degrees = 1 quadrant

4 quadrants = 360 degrees = circle

LIQUID MEASURE

16 ounces = 1 pint

4 quarts = 1 gallon

1 quart = 946.35 milliliters

1000 milliliters = 1 liter

31.5 gallons = 1 barrel (U.S.)

1 liter = 1.0566 quart

4 gills = 1 pint

2 pints = 1 quart

A U.S. gallon is equal to 0.8327 British gallon; therefore, a British gallon is equal to 1.201 U.S. gallons. 1 liter is equal to 1.0567 quarts.

LINEAR MEASURE

1 inch = 2.54 centimeters

40 rods = 1 furlong

8 furlongs = 1 statute mile

12 inches = 1 foot

3 feet = 1 yard

5.5 yards = 1 rod

1 statute mile = 5280 feet

3 statute miles = 1 statute league

1 nautical mile = 6076.042 feet

HOUSEHOLD MEASURES AND WEIGHTS†

Approximate Equivalents: 60 gtt. = 1 teaspoonful

= 5 ml = 60 minims = ⅛ ounce

1 teaspoon = ⅛ fl oz

16 teaspoons (liquid) = 1 cup

3 teaspoons = 1 tablespoon

12 tablespoons (dry) = 1 cup

1 tablespoon = ½ fl oz

1 cup = 8 fl oz

1 tumbler or glass = 8 fl oz; ½ pint

Conversion Rules and Factors

To convert units of one system into the other, multiply the number of units in column I by the equivalent factor opposite that unit in column II.

WEIGHT

1 gram

=

0.03527 avoirdupois ounce

1 gram

=

0.03215 apothecaries' ounce

1 kilogram

=

35.274 avoirdupois ounces

1 kilogram

=

32.151 apothecaries' ounces

1 kilogram

=

2.2046 avoirdupois pounds

1 grain

=

64.7989 milligrams

1 grain

=

0.0648 gram

1 avoirdupois ounce

=

28.3495 grams

1 apothecaries' ounce

=

31.1035 grams

1 avoirdupois pound

=

453.5924 grams

VOLUME (AIR OR GAS)

1 cubic centimeter (cm3)

=

0.06102 cubic inch

1 cubic meter (m3)

=

35.314 cubic feet

1 cubic meter

=

1.3079 cubic yard

1 cubic inch (in3)

=

16.3872 cubic centimeters

1 cubic foot (ft3)

=

0.02832 cubic meter

CAPACITY (FLUID OR LIQUID)

1 liter

=

2.1134 pints

1 liter

=

1.0567 quart

1 liter

=

0.2642 gallon

1 fluid dram

=

3.697 milliliters

1 fluid ounce

=

29.573 milliliters

1 pint

=

473.1765 milliliters

1 quart

=

946.353 milliliters

1 gallon

=

3.785 liters

TIME

1 millisecond = one thousandth (0.001) of a second

1 minute = 1/60 of an hour

1 second = 1/60 of a minute

1 hour = 1/24 of a day

TEMPERATURE †

Given a temperature on the Fahrenheit scale, to convert it to degrees Celsius, subtract 32 and multiply by 5/9. Given a temperature on the Celsius scale, to convert it to degrees Fahrenheit, multiply by 9/5 and add 32. Degrees Celsius are equivalent to degrees Centigrade.

PARTS PER MILLION

ENERGY

1 foot pound = 1.35582 joule

1 joule = 0.2389 Calorie (kilocalorie)

1 Calorie (kilocalorie) = 1000 calories = 4184 joules

A large Calorie, or kilocalorie, is always written with a capital C.

pH

The pH scale is simply a series of numbers stating where a given solution would stand in a series of solutions arranged according to acidity or alkalinity. At one extreme (high pH) lies a highly alkaline solution; at the other extreme (low pH) is an acid solution containing 3.65 g of hydrogen chloride per liter of water. Halfway between lies purified water, which is neutral. All other solutions can be arranged on this scale, and their acidity or alkalinity can be stated by giving the numbers that indicate their relative positions. If the pH of a certain solution is 5.3, it falls between gastric juice and urine on the above scale, is moderately acid, and will turn litmus red.

Tenth-normal HCl

−1.00

Litmus is red in this acid range

Gastric juice

‡ 1.4

Urine

‡ 6.0

Water

7.00

Neutral

Blood

7.35-7.45

Litmus is blue in this alkaline range.

Bile

‡ 7.5

Pancreatic juice

8.5

Tenth-normal NaOH

13.00

‡ These body fluids vary rather widely in pH; typical figures have been used for simplicity. Urine samples obtained from healthy individuals may have pH readings anywhere between 4.7 and 8.0.

Units of Measurement (Including SI Units) is a sample topic from the Taber's Medical Dictionary.